Identity and Inverse Operators

Some operators have a special role in in mathematics, especially in group theory. Two such operators are the identity operator and the inverse operator.

The identity operator

When this operator is applied to something (a number, a shape, an expression, etc.) you get the same thing it was applied to, for example, when the identity operator is applied to the number 3, the result is the number 3. When it is applied to a triangle, you get a triangle.

The inverse operator

Some operators can be paired so that if they are applied one after the other to the operand, it is as if we applied the identity operator to it. We get back the ‘naked’ operand. These pairs of operators are called inverse operators. Here is an example of a pair of inverse operators: “square” and the “positive square root”.
Take the number 2 for example. When you square you get 4. When you take the positive square root of 4 you get back to the original number, 2. This is the same as saying that we applied the identity operator to the number 2. Note that in this case, we need to restrict the group of numbers to the positive numbers because there are two roots to the square root, one positive and one negative.